Ecloud in PS2, PS+, SPS+

We present a preliminary but broad assessment of the ecloud build-up for the various proposed upgrades of the LHC and its injectors. The study pertains only to the ecloud in bending dipole magnets, and does not shed any light on the effects of the electrons on the beam. We focus on the ecloud heat load, although we have computed many other quantities of interest. The basic variable used to classify our results is the bunch spacing tb, whose values are 12.5, 25, 50 and 75 ns. The ecloud heat load follows an inverse relation to tb both for the LHC and for the injectors, with tb = 12.5 ns being by far the least favorable case. Although tb = 75 ns is the most favorable case, the 50-ns option comes closely behind. A simulated comparison of copper vs. stainless steel shows a clear advantage of the former over the latter. Somewhat surprisingly, a comparison of gaussian vs. flat longitudinal bunch profile does not show a clear winner, at least for the LHC at tb = 50 ns. We describe the strengths and limitations of our calculations.